Related papers: Reaction Diffusion TAP
Many complex systems exhibit extreme events far more often than expected for a normal distribution. This work examines how self-similar bursts of activity across several orders of magnitude can emerge from first principles in systems that…
Diffusion is the result of repeated random scattering. It governs a wide range of phenomena from Brownian motion, to heat flow through window panes, neutron flux in fuel rods, dispersion of light in human tissue, and electronic conduction.…
Cross-diffusion systems play a central role in mathematical modelling, in which density-dependent dispersal and multiscale mechanisms can lead to spatial segregation and diffusion-driven instabilities. In several relevant examples,…
The ways in which an innovation (e.g., new behaviour, idea, technology, product) diffuses among people can determine its success or failure. In this paper, we address the problem of diffusion of innovations over multiplex social networks…
We present a mathematical study for the development of multiple sclerosis based on a reaction-diffusion system. The model describes interactions among different populations of human cells, motion of immune cells stimulated by cytokines,…
Understanding the pattern formation in communities has been at the center of attention in various fields. Here we introduce a novel model, called an "information-particle model," which is based on the reaction-diffusion model and the…
The concept of cross diffusion is applied to some biological systems. The conditions for persistence and Turing instability in the presence of cross diffusion are derived. Many examples including: predator-prey, epidemics (with and without…
Understanding how local perturbations induce the transient dynamics of a network of coupled units is essential to control and operate such systems. Often a perturbation initiated in one unit spreads to other units whose dynamical state they…
Diffusion models have revolutionized customized text-to-image generation, allowing for efficient synthesis of photos from personal data with textual descriptions. However, these advancements bring forth risks including privacy breaches and…
We study diffusion-limited coalescence, A+A<-->A$, in one dimension, and derive an exact solution for the steady state in the presence of a trap. Without the trap, the system arrives at an equilibrium state which satisfies detailed balance,…
The origin of life is often approached through the lens of replication, heredity, or molecular specificity. This paper proposes a thermodynamic framework in which the emergence of life is driven by the persistence of reaction pathways that…
A combination of reaction-diffusion models with moving-boundary problems yields a system in which the diffusion (spreading and penetration) and reaction (transformation) evolve the system's state and geometry over time. These systems can be…
Patterns of different symmetries may arise after solution to reaction-diffusion equations. Hexagonal arrays, layers and their perturbations are observed in different models after numerical solution to the corresponding initial-boundary…
A spatio-temporal evolution of chemicals appearing in a reversible enzyme reaction and modelled by a four component reaction-diffusion system with the reaction terms obtained by the law of mass action is considered. The large time behaviour…
Reaction-diffusion equations are widely used as the governing evolution equations for modeling many physical, chemical, and biological processes. Here we derive reaction-diffusion equations to model transport with reactions on a…
Generative models such as diffusion models, excel at capturing high-dimensional distributions with diverse input modalities, e.g. robot trajectories, but are less effective at multi-step constraint reasoning. Task and Motion Planning (TAMP)…
This note shows how classical tools from linear control theory can be leveraged to provide a global analysis of nonlinear reaction-diffusion models. The approach is differential in nature. It proceeds from classical tools of contraction…
The dynamics of a coupled two-component nonequilibrium system is examined by means of continuum field theory representing the corresponding master equation. Particles of species A may perform hopping processes only when particles of…
Widespread interest in the diffusion of information through social networks has produced a large number of Social Dynamics models. A majority of them use theoretical hypothesis to explain their diffusion mechanisms while the few empirically…
The rate of adoption of new information depends on reinforcement from multiple sources in a way that often cannot be described by simple contagion processes. In such cases, contagion is said to be complex. Complex contagion happens in the…